Last week I attended a conference at the Perimeter Institute for Theoretical Physics, titled “Hopf Algebras in Kitaev’s Quantum Double Models: Mathematical Connections from Gauge Theory to Topological Quantum Computing and Categorical Quantum Mechanics”. My flight from LAX (Los Angeles) to YYZ (Pearson-Toronto) was delayed due to a maintenance issue, leaving me sitting in the plane on the tarmac for about an hour and a half before takeoff, right close to midnight. My flight to Oxford for the QPL conference (Quantum Physics and Logic) two years ago had a similarly long delay… Hmmmn. Despite this conference being fairly small—40 people on the list of participants—there were several people present that I met at that QPL conference (Ross Duncan, Stefano Gogioso, and Pawel Sobocinski), and a couple more that I met while I was a grad student at Riverside (Tobias Fritz and Derek Wise). It turns out Ross and Stefano are sharing an apartment on the floor above my room.

Despite the flight delay, I made it to the registration / check-in on time, after putting my luggage away in my 8th floor apartment room. However, by the time I got through registration, everyone else had already migrated over to the Bob room on the 4th floor, where all the talks were held. (There is also an Alice room at the Perimeter Institute.) By the time I found the Bob room, I missed the opening comments and the first five minutes of the first talk. That was the only talk on Monday that I was able to stay awake through, by virtue of the fact that I was standing next to the entrance. I would have liked to have been able to stay awake for more than the first half of each of the remaining talks that day, but exhaustion from a red eye flight is exhaustion from a red eye flight.

Stefano got to the first talk at about the same time I did, and he recognised me before I recognized him. And yes, that variation in spelling is intentional. I got very little out of the talks of the first day, in part because of my sleep situation, but largely because the content is still pretty foreign to me. All the talks were videoed, so I look forward to reviewing them with the benefit of the hindsight of knowing which terms are the actual buzzwords. I walked up to Pawel at the end of the first talk, and he was (pleasantly) surprised to see me. I talked with Tobias during the morning coffee/tea break, and reintroduced myself to Derek. I also made several new connections through the week. An amusing side-note: there were snacks with labels during the various coffee/tea breaks, and on Monday morning the snack label said “Quiche with salsa sauce”. The Dept. of Redundancy Department strikes again!

Since I was sponsored by the Perimeter Institute, I got full Visitor privileges, including an office and a password for the WiFi network. For the entire duration of my stay, I did not have to share my apartment or my office, which made it a lot easier to relax. Since this was my first visit to the Perimeter Institute, I also got some swag—a PI mug with a chalkboard side and a black PI T-shirt. Despite my efforts, I didn’t hit my $50 per diem for meals not included with the conference on any of the days I was there. I think my closest was about $40 on Tuesday. The only thing I was able to put on that account on Monday was two-menu-items dinner (fajita salad and something else).

On Monday evening I got my shortwave radio set up, and fell asleep just after 10:00, right as the program I was waiting for started.

On Tuesday morning I woke up feeling sick in my throat. From that point on I made an effort to ensure I drank plenty of (hot) liquids throughout the week, which helped. I discovered the stairs to my apartment and took them down. I couldn’t figure out why my shoulders were sore until late morning, when I realized I had been carrying my luggage through the airports instead of rolling it. Derek gave the first talk of the day, and it was the only talk of the first two days where I felt like I would be able to understand a paper based on the talk or a paper the talk was based on. By the end of the day I was starting to feel a little guilty for having every aspect of the trip covered by the Perimeter Institute. Didn’t stop me from trying to maximize the benefit I got out of it at the Black Hole Bistro, though.

After the last talk on Tuesday I went outside for some sunlight, but found the WiFi does not reach very far outside at all. So I went back inside and collaborated a bit with Tobias and Lucy Zhang. A couple of people stayed outside a while longer when suddenly weather attacked. It was sunny one minute, pouring the next, and hailing shortly after that. They were trapped underneath the patio umbrella until someone with a golf umbrella saved them. One of the waitresses at the Black Hole Bistro took video of the rescue on her tablet and later showed it to her coworkers that missed the saga.

Tuesday evening was the last time I used the elevator to get to my apartment. After that I exclusively used the stairs.

I woke up at 3:00 Wednesday morning, and could not get back to sleep. Once it was light enough outside, I walked around Silver Lake, the artificial mill pond between my apartment and the Perimeter Institute. I took a bunch of pictures on my cell phone—that was basically the only function that still worked, since I was outside the service area—but apparently I forgot to save a bunch of them.

Wednesday seemed to be Graphical Calculi day. Ross described the state of the ZX art. A recent completeness result from June is exciting, even if it isn’t yet formulated in a “natural” way. On one of the earlier slides discussing the computer sciency motivation, a code snippet was included that several people missed:

fun fact 0 = 1

| fact x = x * fact (x-1)

… defining the factorial function. I was highly amused at the first line stating a rather curious fun fact, and I suspect that was a strong influence on Ross’s decision to include that particular snippet.

Having looked at the ZX calculus for comparisons with my dissertation work, this was the first talk of the conference where I felt like I actually understood the language being spoken. And I understood it well enough to ask a well-formed question (Do you have confluence in the diagram rewrites?). After lunch Pawel gave his talk on graphical linear algebra. The parallels to my dissertation are even more clear here, to the extent that it was cited in Pawel’s slides.

The poster session followed the break after Pawel’s talk. I didn’t understand the work being presented well enough to even ask where to start. So after giving the posters some cursory attention, I started talking with Pawel and Derek. The conference banquet followed the poster session, and I helped entertain the people at my table with puns (and co-puns). I had a glass of white wine that was paired with the appetizer and a glass of rosé that was paired with the main course. The tannins in the rosé clearly stated themselves without being overbearing. Quite pleasant.

Sprinkled through the week were “free discussion”s. I made a joke about the “free” part of free discussion that got repeated several times by people other than me (free discussions are discussions without any equations (alternatively, relations)). I found out about the oft repetition on Wednesday evening, when I went to Jane Bond’s, a bar in Waterloo, with Pawel, Ross, and Andreas Bauer. We sat in the patio, and generally talked politics (UK, US, world). As a group, we got four rounds of beer (all IPAs), though I only participated in the first and third rounds.

After we finished after the last call, we walked to Ethyl’s Lounge, which was closed—it was 2 a.m., after all. Ross aimed us back towards the Perimeter Institute, where we could navigate back to our respective hotels / apartments. Unfortunately he got lost. Fortunately I recognized that we were next to Silver Lake when he admitted being lost. Having gone around the lake within the previous 24 hours, I was able to lead the group back.

Burak Sahinoglu gave the first talk on Thursday. I think I would have understood more of Monday and Tuesday’s talks if they had been preceded by Burak’s talk. Incidentally, Burak’s home institution is CalTech, so we are not far separated in terms of location. Tobias was up next, and the last feelings of guilt I had about the trip vanished when I saw my name included on the first slide. Being referenced in 2/18 talks is not insignificant.

During an afternoon break I located the nearest Erb St sign and attempted to take some cellfies that included the sign. The root of Erbele is Erbe, not Erb, but it’s close enough to be amusing. After failing to get a good photo, I asked Ross to take the picture for me. Between the street sign and the Perimeter Institute is a clay and glass shop, and I bought a couple of glass birds to give as gifts.

The last talk on Thursday was AWESOME. Even before QPL 2015, I was trying to visualize some of the equations of Hopf algebras as a 3D animation. I have the pictures in mind, but I don’t have the TikZ chops to draw it in LaTeX. David Reutter’s talk jumped straight from categories to 3-categories, showing how the various string diagram equations are shadows of 3D structures. The take-home message was to more fully use the interplay between algebra and topology: roughly, lower dimension topology = complicated algebra; higher dimension topology = simple algebra. Traditional notation has linear topology, so we can simplify by going to 2D and 3D. During the free discussion, some of us were pondering how the 3D diagrams should get published… multilayered transparencies? pop-up book style? 3D printer code? With interactive PDFs, the electronic versions could have some killer diagrams. But again, what helper(s) should be used to draw the 3D diagrams?

The conference photo was taken on Tuesday, before lunch, and was sent to all the participants on Friday morning before the first talk. After the two Friday talks there was a chaired discussion that exceeded the (low) expectations everyone I talked to had for it. For me it started on a high note, with the graphical calculus side of things. It sounds like, at least, almost everyone is a closet user of some kind of graphical calculus, so why isn’t graphical notation more universally seen (e.g. in publications)? The main objections to universal graphical calculi that I heard were threefold: it’s hard to draw, it’s hard to manipulate the drawings, it doesn’t scale well. The first two objections can already largely be overcome with assistants like Globular and Quantomatic. Both of those links are to the respective arXiv articles describing their functionality.

I have not used either of these assistants, but I can think of a few things I would want on my wish list for such assistants: some kind of automation for drawing a diagram, given some traditional (1D) input (possibly specifying what kind of traditional notation is being used and what kind of graphical notation to output); some kind of export diagrams to LaTeX option (e.g. TikZ); and some kind of automated diagram simplification that allows the user to see the diagram at each step after the simplification process ends (whether by lack of further simplifications possible or by user input if things get too hairy). Ideally, each step of the automated simplification would have an export to LaTeX option.

There was much more discussed in the chaired discussion, but I don’t recall the other parts clearly.

Afterwards, I got my luggage packed again, in preparation for an early morning flight home. The Black Hole Bistro was closed for dinner on Friday, apparently because of some kind of holiday on Monday. The U.S. doesn’t have any August holidays, but apparently Canada does. David, Derek, Stefano and I had dinner together at Abe Erb’s. I decided to have the distinctly Canadian dish, poutine. Traditionally, poutine is french fries topped with gravy and curds. The variation I had had cheese instead of curds, and chopped green onions on top of everything. Apparently the name “poutine” is Quebec slang for “a mess”, which seems altogether appropriate. After poutine, I went back to Jane Bond’s to say farewell to the bunch of conference attendees that converged there.

The flight back was fairly uneventful, aside from the question mark over whether I would be able to get on the flight at all. There were some weather issues on Friday that caused some flights to be cancelled, and presumably because of that (I didn’t actually ask), my flight was overbooked. Somehow, despite being overbooked, I ended up with an empty seat next to me. One of the in-flight movie options was The Magnificent Seven, and I was momentarily excited to be able to watch a Clint Eastwood film I haven’t gotten around to watching yet. I watched the trailer and saw it was a remake, so I passed on it.

I’m back in California now. It was a fun workshop and a fun trip. I’m glad I went.

Some additional amusing anecdotes that didn’t find their way into the above storyline:

Inside PI, near the entrance, there is a glass wall with lots of mathsy/physicsy scribbles on it, and markers nearby to encourage further such scribblings. One such said, “p = np for n=1”, which ought to be revised, either to append “or p=0” or replacing “n=1” with “n a projection operator onto the p-axis”. It should also be noted that there are chalkboards EVERYWHERE, so the markers on the glass panel/wall is a natural extension.

After the sudden hailstorm (which died just as suddenly, after the patio umbrella got knocked over by the hail), it was sunny again. It was deemed a good time to get back to our apartments because “the current rain is zero, but the normalized potential rain is nonzero.” Admittedly, it wasn’t my best pun of the week.